Filter formulation and wavefield separation of cross-well seismic data

Multichannel filtering to obtain wavefield separation has been used in seismic processing for decades and has become an essential component in VSP and cross-well reflection imaging. The need for good multichannel wavefield separation filters is acute in borehole seismic imaging techniques such as VSP and cross-well reflection imaging, where strong interfering arrivals such as tube waves, shear conversions, multiples, direct arrivals and guided waves can overlap temporally with desired arrivals. We investigate the effects of preprocessing (alignment and equalization) on the quality of cross-well reflection imaging wavefield separation and we show that the choice of the multichannel filter and filter parameters is critical to the wavefield separation of cross-well data (median filters, f–k pie-slice filters, eigenvector filters). We show that spatial aliasing creates situations where the application of purely spatial filters (median filters) will create notches in the frequency spectrum of the desired reflection arrival. Eigenvector filters allow us to work past the limits of aliasing, but these kinds of filter are strongly dependent on the ratio of undesired to desired signal amplitude. On the basis of these observations, we developed a new type of multichannel filter that combined the best characteristics of spatial filters and eigenvector filters. We call this filter a ‘constrained eigenvector filter’. We use two real data sets of cross-well seismic experiments with small and large well spacing to evaluate the effects of these factors on the quality of cross-well wavefield separation. We apply median filters, f–k pie-slice filters and constrained eigenvector filters in multiple domains available for these data sets (common-source, common-receiver, common-offset and common-midpoint gathers). We show that the results of applying the constrained eigenvector filter to the entire cross-well data set are superior to both the spatial and standard eigenvector filter results.